A143545 -id:A143545 - cp's OEIS frontend

A282028 If n is prime then a(n) = 2n, otherwise a(n) is the smallest missing number.

0, 1, 4, 6, 2, 10, 3, 14, 5, 7, 8, 22, 9, 26, 11, 12, 13, 34, 15, 38, 16, 17, 18, 46, 19, 20, 21, 23, 24, 58, 25, 62, 27, 28, 29, 30, 31, 74, 32, 33, 35, 82, 36, 86, 37, 39, 40, 94, 41, 42, 43, 44, 45, 106, 47, 48, 49, 50, 51, 118, 52, 122, 53, 54, 55, 56, 57, 134, 59, 60, 61, 142, 63, 146, 64, 65

Offset: 0

N. J. A. Sloane, Feb 16 2017

nonn

N. J. A. Sloane, Table of n, a(n) for n = 0..10000

Cf. A000720, A127202, A143545, A280985, A282029.

first(n) = { my(res = vector(n), i = 1); for(x=1, n-1, if(isprime(x), res[x+1] = 2*x, if(setsearch(Set(res), i), i++); res[x+1]=i; i++)); res; } \\ Iain Fox, Nov 18 2017

If n is prime, a(n) = 2n, and these points line on the upper straight line in the graph.
If n is not a prime, after n terms we have seen all the numbers from 0 through a(n) and also the doubles of all the primes p in the range a(n)/2 < p < n.
So n = a(n) + pi(n) - pi(a(n)/2). In other words, if n is not a prime then a(n) is the unique solution to a(n) - pi(a(n)/2) = n - pi(n).
This implies that if n is not a prime, a(n) = n*(1 - 1/(2*log(n)) + o(1/log(n))).
These are the points on the lower line, which is not straight but has slope roughly equal to 1.

A143544 Triangle read by rows, T(n,k) = 2 if n is prime, 1 otherwise; 1<=k<=n.

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Gary W. Adamson, Aug 23 2008

Row sums = A143545: (1, 4, 6, 4, 10, 6, 14,...) = componentwise addition of (1, 2, 3, 4, 5,...) and A061397: (0, 2, 3, 0, 5, 0, 7,...).

			First few rows of the triangle =
1;
2, 2;
2, 2, 2;
1, 1, 1, 1;
2, 2, 2, 2, 2;
1, 1, 1, 1, 1, 1;
2, 2, 2, 2, 2, 2, 2;
...

Michael De Vlieger, Table of n, a(n) for n = 1..11325

Cf. A010051, A061397, A143536, A143545.

Table[1 + Boole[PrimeQ[n]], {n, 11}, {k, n}] // Flatten (* Michael De Vlieger, Oct 31 2021 *)

Triangle read by rows, T(n,k) = 2 if n is prime, 1 otherwise; 1<=k<=n.

T(n, k) = A143536(n, k) + 1. - Georg Fischer, Oct 31 2021

A282462 Integers but with the primes cubed.

Original entry on oeis.org

0, 1, 8, 27, 4, 125, 6, 343, 8, 9, 10, 1331, 12, 2197, 14, 15, 16, 4913, 18, 6859, 20, 21, 22, 12167, 24, 25, 26, 27, 28, 24389, 30, 29791, 32, 33, 34, 35, 36, 50653, 38, 39, 40, 68921, 42, 79507, 44, 45, 46, 103823, 48, 49, 50, 51, 52, 148877, 54, 55, 56

Offset: 0

Vincenzo Librandi, Feb 17 2017

			a(4) = 4 because 4 is composite.
a(5) = 125 because 5 is prime and 5^3 = 125.

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Cf. A061397, A103164, A143545.

[0] cat [IsPrime(n) select n^3 else n: n in [1..60]];

Mathematica
```
Join[{0},If[PrimeQ@#,#^3,#]&/@Range@80]
```

cp's OEIS Frontend

A282028 If n is prime then a(n) = 2n, otherwise a(n) is the smallest missing number.

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A143544 Triangle read by rows, T(n,k) = 2 if n is prime, 1 otherwise; 1<=k<=n.

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A282462 Integers but with the primes cubed.

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